find the smaller of 2 consecutive integers, x, if the sum of the smaller and 6 times the larger is - 29

Answer: - The smaller integer is - 5.

Explanation:-

Let the first consecutive integer be x and the second consecutive integer be x+1.

According to the given question:-

x+6 (x+1) = - 29

⇒x+6x+6 = - 29 [distributive law]

⇒x+6x = - 29-6 [subtract 6 on the both sides]

⇒7x = - 35 [combining like terms ]

⇒x = - 5 [dividing 7 on both sides]

Thus the smaller integer = x = - 5

larger integer = x+1 = - 5+1 = - 4